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Journal of Applied Mathematics and Physics, 2014, 2, 930-937

Published Online September 2014 in SciRes. http://www.scirp.org/journal/jamp http://dx.doi.org/10.4236/jamp.2014.210105 

How to cite this paper: Carrillo-Inungaray, M.L., et al . (2014) Effect of Temperature, pH and Water Activity on Penicillium

digitatum Growth. Journal of Applied Mathematics and Physics, 2, 930-937. http://dx.doi.org/10.4236/jamp.2014.210105 

Effect of Temperature, pH and Water Activity on Penicillium digitatum Growth

María Luisa Carrillo-Inungaray1*, Madeleine Hidalgo-Morales2,Guadalupe del Carmen Rodríguez-Jimenes2, Miguel Ángel García-Alvarado2,Mario Ramírez-Lepe2, Abigail Reyes Munguía1, Victor Robles-Olvera2 1Universidad Autónoma de San Luis Potosí, Ciudad Valles, México

2Unidad de Investigación y Desarrollo en Alimentos, Instituto Tecnológico de Veracruz, Veracruz, México

Email:*maluisa@uaslp.mx 

Received 9 July 2014; revised 12 August 2014; accepted 21 August 2014

Copyright © 2014 by authors and Scientific Research Publishing Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/ 

 Abstract

Growth curves fitted Penicillium digitatum were used to analyze the effect of temperature, pH andaw  on their growth. To asses observance of independent variable effects on all growth parameters( λ, latency time,  μ, growth rate and y max maximal growth) a slow growth strain of P. digitatum wasemployed. Growth curves were obtained at different conditions of temperature (10˚C  - 40˚C), pH(3.0 - 7.0) and water activity (0.800 - 0.990) and growth parameters were calculated by fitting oflogistic model. Polynomial models were made by linear regression and all terms (linear, quadraticand interactive effects) were statistically significant (p < 0.001). All growth parameters, includingmaximal growth were affected by environmental conditions; pH effect was more important onmaximal growth than that on lag time or growth rate. In some aspects results and modeling beha-vior of P. digitatum, are very similar to modeling of bacterial growth.

Keywords

Fungi Growth Model, P . Digitatum, Slow Growth, Food Safety, Food Spoilage

1. Introduction

The consumers claim for foods gently processed with a minimum content of preservatives. In attention to these

demands and in order to have safe foods, a high value of one “hard” preservative has been replaced by low val-

ues of several “gentle” preservative factors to reach the same preservative effect that in traditionally prepared

foods.

*Corresponding author.

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To test microbial behavior at these new environmental food conditions, mathematical models developed in

 predictive microbiology have demonstrated a useful tool to avoid the application of fastidious and expensive

microbiological methods. Most models commonly used are polynomial expressions where growth response is a

function of environmental growth factors. Predictive polynomial models of food borne or spoilage bacteria relating growth to temperature, pH, water

activity (aw) and others factors are in literature [1]-[3]. Statistical analysis of these models shows that commonlyinteractive and quadratic effects are significant; and from data analysis is possible to verify that effects of factor

on growth parameters of slow growth strains are less important than those observed on fast growth strains.

Knowledge about interactive effects of these factors on fungi growth has not been extensively documented as

that on bacterial growth. Furthermore, it is important to analyze the models with the factors of accuracy and bias

for the possible discrepancy between observed and predicted values obtained with a model. 

Fungi are widely distributed in nature and their prevalence is one of the major causes of food spoilage  [4], 

moreover fungi presence can carry out mycotoxin production [5], therefore their control is necessary in order to

have a safe food product [6]. There are some models in literature relating fungi growth to aw [7] [8] or aw and

temperature [1] [6] [9] [10]. The pH effect on fungi growth has not been widely studied and controversial results

have been published. Some authors reported that pH effect was not significant whereas a variable effect was

found by others [11] [12]; moreover existence [13] or not existence [6] [11] of pH significant interactive effects

has been reported too. Under this controversial find it is evident that more studies about effect of pH and theirinteractions with other factors are necessary. Otherwise, information about the effects of factors on relatively

slow growing fungi is not available. It is important to know behavior of slow growing fungi because they can

start to growth during predicted food shelf time if bacterial growth is controlled. Moreover, factors effect is

more confused with slow growth strains that fast strains because response to factors may be masked by inherent

fast growth rate of fast strains. Penicillium digitatum —a deuteromycetus fungus of hiphomycetal class, one of

the most common post-harvest pathogens causing green mold rots in citrus fruits  [5] [14] —grows relatively

slower than other deteriorative molds [15]-[18]. 

The novelty of this work is to identify the important factors to consider building a predictive model; since it is

 possible that a rapid growth rate in microorganisms could mask the significant effects of environmental factors

and their interactions. Therefore, the objective of this work was to analyze the effect of growth factors and their

interactions on slow growing fungi by modeling the Penicillium digitatum growth in temperature, aw  and pH

growth ranges reported for this fungus.

2. Materials and Methods

2.1. Experimental Design

Growth kinetics of Penicillium digitatum were obtained at conditions of water activity (0.800, 0.895 and 0.990)

and pH (3.0, 5.0 and 7.0) established by a centered sides design: 2k  + 2k + 1 [19]; inoculated media were incu-

 bate at 10˚C, 20˚C, 30˚C, and 40˚C. Factors limit values were elected considering minimum and maximum re-

 ported values for P. digitatum growth. All experiments were performed in duplicated.

2.2. Media Preparation

Saboraud dextrose agar (Bioxon) was prepared following manufacturer’s instructions. Norrish [20] and Ross [21] 

equations were employed to calculate sucrose (Hycel) needed to reach the desired aw; pH was adjusted by addi-

tion of citric acid (Baker) 10% (p/v). Sterilized and acidified agar was aseptically distributed in petri dishes.

2.3. Preparation of Inoculum

Penicillium digitatum was isolated from spoiled citrus fruits and identified according to Samson et al. [22]. The

strain was cultured in Saboraud dextrose agar slants and incubated at 25˚C for 7 days. A spore suspension was

 prepared by overlaying sporulated cultures with 10 mL of sterile distilled water. The spore suspension was used

immediately.

2.4. Inoculation

The spore suspension (approximately 103  spores) was centrally inoculated in petri dishes by pouring 2 µL as

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was indicated by Fustier et al.  [23]  to give a circular inoculum of 2.5 mm of diameter. The inoculated plates

were incubated for 20 days in hermetically closed plastic containers to avoid dehydration.

2.5. Fit of Fungi Growth Curves

The colony size increase was followed by measuring colony diameter every day and this was plotted versus in-cubation time. Growth parameters were calculated by fitting of logistic equation (Equation (1)):

( )max

max

max

0

1 1 e   n A t 

 y y

 y

 y

µ −

=

+ −

  (1)

where ( )  ( )

( )

0,

,n

t  A t 

t t 

λ 

λ λ 

≤= 

− ≥, max y   is maximum growth; 0 y , initial inoculums; maxµ  , growth rate and

( )n A t    is a discontinuity in the time.

2.6. Model Development

Polynomial models relating natural logarithm of   P. digitatum growth parameters (growth rate, lag time andmaximum growth) to temperature, aw and pH were built by linear regression. Natural logarithm of growth para-

meters was choose with the purpose of diminish variance and avoid negative lag phases.

2.7. Performance Analysis of Models

Models were analyzed by the accuracy (  AF  ) (Equation (2)) and bias factors (  BF  ) (Equation (3)), introduced

 by Ross [24], modified by Baranyi et al. [25] and as were used by López et al. [26]. These factors were calcu-

lated as follow:

( )2

1exp

n

k 

 LnP LnO

 AF n

=

−

=

∑  (2)

( )1exp

n

k 

 LnP LnO

 BF n

=

−

=

∑  (3)

were P and O are predicted and observed values, respectively, and n is the experimental points number. A bias

factor value greater than 1 indicate that, on average, predicted are greater than observed values; otherwise, an

accuracy factor of 1 indicate a good concordance between predicted and observed values.

3. Results and Discussion

Below are presented the results of the effect of temperature, pH and water activity on Penicillium digitatum-growth.

3.1. Results of Penicillium digitatum Growth

P. digitatum growth was observed in 23 of 36 experimental conditions. Not growth was reported when lag time

was prolonged after an incubation time of 20 days and this occurred at extremes experimental conditions of

temperature, aw or pH. Except for lag time, each growth phase was well described by growth curves and their

shape was concordant with experimental conditions. Generally, when two factors remain constant, effect of third

factor gave curves sufficiently separates to observe effect levels of such factor. Consequently, calculated growth

 parameters (Table 1) were coherent and, as it was expected, minimal and maximum growth were observed at

extreme and central conditions, respectively.

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Table 1. Growth parameters of Penicillium digitatum at different experimental conditions calculated by logistic model.

Condition Growth parameter

T aw   pH (h) (mm⋅h−1)  ymax (mm)

10 0.990 3 106.74 0.009 8.49

10 0.990 5 99.732 0.017 7.27

10 0.990 7 292.95 0.023 5.88

20 0.800 5 221.22 0.017 6.12

20 0.800 7 147.97 0.017 13.79

20 0.895 3 112.91 0.009 8.04

20 0.895 5 48.409 0.015 11.17

20 0.895 7 65.246 0.017 14.58

20 0.990 3 6.7422 0.018 26.37

20 0.990 5 5.8246 0.032 21.23

20 0.990 7 15.819 0.041 16.17

30 0.800 5 55.023 0.022 9.2830 0.800 7 34.029 0.021 19.66

30 0.895 3 33.939 0.012 10.83

30 0.895 5 13.454 0.019 14.11

30 0.895 7 16.765 0.020 17.39

30 0.990 3 2.2646 0.022 29.69

30 0.990 5 1.8088 0.038 22.49

30 0.990 7 4.5418 0.047 16.12

40 0.800 7 41.609 0.016 10.17

40 0.990 3 4.0443 0.017 12.13

40 0.990 5 2.9867 0.028 8.64

40 0.990 7 6.9338 0.033 5.83

3.2. Results of Factors Effect on Lag Time

Lag time was measured in most cases where growth was observed, and it was as long as 293 h at extreme condi-

tions. Not correlation was found between lag time and growth rate but generally slowest growth rates match

with long latency times and small maximal growth. Temperature increases of 10˚C caused not proportional re-

duction of latency times, at pH 3 and aw 0.990, lag times are 16 times longer at 10˚C than at 20˚C, and 3 times

longer at 20˚C than 30˚C, but around 0.5 times at 30˚C than at 40˚C. In most conditions, at same temperature and

aw values, lag times are longer at extreme pH (3 and 7) than at central value (pH 5). Repeatedly, lag times are two

or three times longer at pH 7 than a pH 5; whereas those obtained at pH 3 are bigger but very close to those cal-

culated at pH 5 (except for 0.895 aw). Otherwise, lag times are progressively shorter as aw values are increased.

3.3. Results of Factors Effect on Growth Rate

In all tested conditions, growth rates were generally smaller than those reported for other deteriorative fungi [9] 

[11] [15] even 10 times smaller than other P. digitatum strains reported by Plaza et al. [19] and Dantigny et al.

[27]. These differences between growth rates observed and those reported in literature can be related primarily

to differences between strains nature.

Growth rate of P. digitatum showed an optimum temperature value between 20˚C and 30˚C, similar to these

reported by Plaza et al.  [18].  It was noted that P. digitatum  tolerance to experimental extreme temperatures

(10˚C and 40˚C) increased when aw values were increased. Growth rates obtained at pH 5 and 7 were very simi-

lar and higher than those observed at pH 3. These results are concordant with that published by Neumeyer’s

team [28] who established that Pseudomonas growth rate is unaffected by pH in the range pH 5.4 to 8.6. Similar

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results have been reported for fungi growth [5] [11] [12], in general, when pH interval studied is around of op-

timal pH range for microorganism growth, not significant lineal or interactive effects were found regardless of

acids nature (acetic, lactic, phosphoric, citric or hydrochloric acids) used to adjust pH. Otherwise, significant ef-

fects were reported when pH range studied is far of optimal region for growth when potassium citrate [13] was

used to buffering media in a pH range of 2.8 to 3.3. With this arguments and bearing in mind the parabolic clas-

sic shape obtained when pH is plotted versus growth rate, it is logic to find significant effects when all pHgrowth range is analyzed. Besides pH interval studied or nature of acid used to adjust pH, differences between

effects could be due also to inherent acid tolerance and optimal growth pH of each microorganism.

3.4. Results of Factors Effect on Maximal Growth

Maximal growth was observed at 30˚C, pH 3 and 0.990 aw values and this growth parameter increased as pH or

aw values were augmented. These results are interesting because maximal growth is commonly limited by nu-

trient availability or toxic metabolites accumulation, and its maximal value is finally reached earlier or later ac-

cording to lag time and growth rate. In consequence, frequently this growth parameter does not show correlation

with environmental factors, in fact, it is common to find in literature only lag time and growth rate models.

3.5. Results of Analysis and Performance of Developed Models

Since P. digitatum  is a citrus spoilage fungus, a predictive model of P. digitatum  growth on citrus products

should be expected. In this sense, data for building model should be obtained from P. digitatum growth on a

medium of a citrus similar composition, However, when models are created of this way, levels of independent

variable, as pH or aw, are restricted by food nature (because its stability can be affected); consequently, effects of

independent variables cannot be quantified. Therefore, to measure the effect of studied variables, laboratory

culture media are the best option, although the model applicability obtained by this way is limited and validation

tests are necessary before model use. Because the objective of this paper was to analyze independent variables

effect, this last strategy to develop models was used in this work.

Coefficients of polynomial models developed are presented in Table 2. Statistical analyses of model terms

demonstrate that all effects were significant ( p < 0.0001). Lag phase, growth rate and maximum growth were

mainly affected by temperature, whereas the effect of aw and pH are smaller. In all cases, aw and pH interaction

exerts smaller effects than those produced by temperature. Models can predict correctly growth rate and maxim-

al growth but a more important discrepancy is observed for lag time, these observations were confirmed by ac-

curacy and bias factors (Table 3). Accuracy factor for growth rate model was the closest to 1, whereas this fac-

tor indicate not good relation between observed and predicted lag time values. Otherwise, the bias factor of three

models was 1, which indicates that on average, none model underestimates or overestimates growth parameters.

Table 2. Coefficients of regression of polynomial models for each P. digitatum growth parameter.

Polynomial model:

0 1 2 3 4 5

2 2 2

6 7 8 9

 pH pH

 pH pH

w w

w w

 y T a T a T 

a T a

 β β β β β β 

 β β β β 

= + × + × + × + × × + × ×

+ × × + × + × + × 

Parameter maxln y   lnµ    lnλ  

 β 0  −22.235 31.681 24.508

 β 1  0.461 0.189 −0.631

 β 2  19.903 −89.292 19.397

 β 3  2.833 −0.030 −4.791

 β 4  −0.188 −0.044 0.117

 β 5  −0.003 −0.002 −0.004

 β 6  −2.854 0.744 3.687

 β 7  −0.005 −0.002 0.008

 β 8  2.613 50.122 −33.136

 β 9  −0.007 −0.045 0.143

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Table 3. Accuracy and bias factors of polynomial models of  P. digitatum growth.

Model Accuracy factor Bias factor

µ 1.28 1.00

λ 2.43 1.00

 ymax  1.51 1.00

Predicted curves are generally described between replicates and the variability observed is product of varia-

 bility propagation of each predicted growth parameter. As was established previously, the more important dis-

cordance between observed and predicted values was obtained with latency model, results of this nature are

commonly observed in lag time models for bacterial growth models. This discordance is originated by high va-

riability of observed lag time. A more important variability has been previously reported for lag time than for

growth rate [29] and it has been explained because growth rate is one implicit characteristic of the microorgan-

ism, while lag time is more affected by not controlled variables [30] [31] such as time and environmental history.

4. Conclusion

These results suggest that implicit growth rate is an important factor to take into account when a strain is elected

to build a predictive model; it is possible that a fast growth rate could mask significant effects of environmental

factors (such pH) as well as their interactions. These results showed that pH exerts a significant effect, further-

more, interactive and quadratic effects are too significant—at least when citric acid is used to adjust pH, and

they are regularly underrated when fungi growth models are developed. Since the most important effect of pH is

observed on maximal growth, it is important to verify nonexistence of factor effects before omitting the model-

ing on this growth parameter. Nevertheless, further studies on effect of undissociated acid concentration and na-

ture of acid and solute employed to adjust pH and aw, are necessary.

 Acknowledgements

Authors would like to tanks Universidad Autónoma de San Luis Potosí, toallstaff at Unidad de Investigación y

Desarrollo en Alimentos of Instituto Tecnológico de Veracruz and to Consejo Nacional de Ciencia y Tecnología

(CONACyT), México, for their support for this work.

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